Tensor Distribution Function in Multiple Shell High Angular Resolution Diffusion ImagingTensor Distribution Function in Multiple Shell High Angular Resolution Diffusion ImagingLiang Zhan1, Alex D. Leow2,3, Iman Aganj4, Christophe Lenglet4,5, Guillermo Sapiro4,Essa Yacoub5 , Noam Harel5, Arthur W. Toga1, Paul M. Thompson1

1Laboratory of Neuro Imaging, Dept. of Neurology, UCLA School of Medicine, Los Angeles, CA, USA2Department of Psychiatry, University of Illinois at Chicago, USA3Community Psychiatry Associates, USA4Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA5Center for Magnetic Resonance Research, University of Minnesota, Minneapolis, MN, USA

INTRODUCTION

METHODS

Diffusion tensor imaging (DTI) reveals white matter microstructure and fiber pathways in the living brain by examining the 3D diffusion profile of water molecules in brain tissue. Even so, DTI-derived measures are incorrect where fibers cross or mix, as the single tensor model cannot resolve these more complicated white matter configurations. Diffusion spectrum imaging (DSI) avoids this issue by direct model-free Fourier inversion of the diffusion signal, butis time intensive, as it measures the signal using 6D Cartesian sampling [1]. An alternative approach based on sampling only on one or multiple spherical shells in q-space has been proposed, referred to as high angular resolution diffusion imaging [2]. Each spherical shell is a 2D manifold with a specific b-value [3], and the required sampling grows quadratically with the desired angular resolution, as opposed to cubically with the spatial and q-space resolutions in DSI[4]. In this study, we illustrated how to manipulate multiple shell HARDI data using the Tensor Distribution Function (TDF) [5].

A healthy human brain was scanned using a singly refocused 2D single shot spin echo EPI sequence at 7 Tesla. Image parameters were: FOV: 192x192 mm^2 (matrix: 196x96) to yield a spatial resolution of 2x2x2 mm^3, TR/TE 4800/57 ms, acceleration factor (GRAPPA) of 2, and a 6/8 partial Fourier transform was used along the phase encoding direction. Diffusion-weighted images were acquired at three b-values of 1000, 2000 and 3000 s/mm^2 with 256 directions, along with 31 baseline images. EPI echo spacing was 0.57 ms, with a 2895 Hz/Px bandwidth. We modeled the HARDI signal as a unit-mass probability density on the 6D manifold of symmetric positive definite tensors, yielding a continuous mixture of tensors, at each point in the brain [5]. The TDF can model fiber crossing and non-Gaussian diffusion. From the TDF, one can derive analytic formulae for the water displacement probability function, orientation distribution function (ODF), tensor orientation distribution (TOD), and corresponding anisotropy measures. Here we further develop the TDF framework for multi-shell HARDI (Figure 1).

RESULTSFigure 2 shows ODFs for different shells and also multiple shell in an axial section. The color in the ODF plot indicates the directions: red corresponds to medial-lateral, green to anterior–posterior, and blue to superior–inferior orientations. Low b-value data gave a noisier ODF plot, while high b-value data gave partial information loss in fiber crossing regions. The multiple-shell ODF addresses these two disadvantages by integrating all information from different shells..

The tensor distribution function is a powerful signal reconstruction method that can resolve intravoxel fiber crossing in multiple shells HARDI, combining the information obtainable from different shells and boosting detail compared with single-shell HARDI acquisitions.References: 1. Wedeen VJ, Hagmann P, Tseng WI, Reese TG, Weisskoff RM. Mapping complex tissue architecture with diffusion spectrum magnetic resonance imaging. Magnetic Resonance in Medicine. 2005;54(6):1377–1386. 2. Tuch DS, Reese TG, Wiegell MR, Makris N, Belliveau JW, Wedeen VJ. High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity. Magnetic Resonance in Medicine. 2002;48(4):577–582. 3. LeBihan D. 1990. Magnetic resonance imaging of perfusion. Magnetic Resonance in Medicine 14(2): 283-292.4. I. Aganj, C. Lenglet, G. Sapiro, E. Yacoub, K. Ugurbil, and N. Harel, ``Reconstruction of the orientation distribution function in single and multiple shell q-ball imaging within constant solid angle,'' Magnetic Resonance in Medicine, 2010, to appear.5. Leow, AD. (2009), 'The tensor distribution function', Magnetic Resonance in Medicine, vol. 61, no. 1, pp. 205-214.

CONCLUSION

Author: Liang Zhan liang.zhan@loni.ucla.edu Laboratory of Neuro Imaging, 635 Charles E. Young Drive South, Suite 225, Los Angeles, CA 90095